{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ARBFFBDNZ3KZRZMIP7D7AYFO5L","short_pith_number":"pith:ARBFFBDN","schema_version":"1.0","canonical_sha256":"044252846dced598e5887fc7f060aeeacf33ed3a41504a20f8591c69b93c66ba","source":{"kind":"arxiv","id":"2506.02778","version":1},"attestation_state":"computed","paper":{"title":"Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Ostermann, Gangfan Zhong, Qiumei Huang","submitted_at":"2025-06-03T11:57:21Z","abstract_excerpt":"We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semilinear evolution equations with operators having non-dense domain. In particular, we investigate nonsmooth data error estimates for the Allen-Cahn and the Burgers' equation. As an application, we apply these nonsmooth data error estimates to split exponential integrators and derive a convergence result in terms of the data."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.02778","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T11:57:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"846e092ba13d56aa66117c6ee2c177f8e41f2fdba61e11646c2116dab78e410a","abstract_canon_sha256":"772e8b2d8eecc207dff45034a1cbda0484a520290353a730b4a4b2639a58fce7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:11:55.812597Z","signature_b64":"6d75Yp+64LdTJrXdNEGx5xUrThzl1wMOUOq/go1n5XN6sSR5M1kuTIVvP9OB1Oj57rvR4N5pDzqrEEC93GasCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"044252846dced598e5887fc7f060aeeacf33ed3a41504a20f8591c69b93c66ba","last_reissued_at":"2026-06-23T01:11:55.812041Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:11:55.812041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Ostermann, Gangfan Zhong, Qiumei Huang","submitted_at":"2025-06-03T11:57:21Z","abstract_excerpt":"We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semilinear evolution equations with operators having non-dense domain. In particular, we investigate nonsmooth data error estimates for the Allen-Cahn and the Burgers' equation. As an application, we apply these nonsmooth data error estimates to split exponential integrators and derive a convergence result in terms of the data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02778","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02778/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.02778","created_at":"2026-06-23T01:11:55.812112+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02778v1","created_at":"2026-06-23T01:11:55.812112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02778","created_at":"2026-06-23T01:11:55.812112+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARBFFBDNZ3KZ","created_at":"2026-06-23T01:11:55.812112+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARBFFBDNZ3KZRZMI","created_at":"2026-06-23T01:11:55.812112+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARBFFBDN","created_at":"2026-06-23T01:11:55.812112+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L","json":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L.json","graph_json":"https://pith.science/api/pith-number/ARBFFBDNZ3KZRZMIP7D7AYFO5L/graph.json","events_json":"https://pith.science/api/pith-number/ARBFFBDNZ3KZRZMIP7D7AYFO5L/events.json","paper":"https://pith.science/paper/ARBFFBDN"},"agent_actions":{"view_html":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L","download_json":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L.json","view_paper":"https://pith.science/paper/ARBFFBDN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02778&json=true","fetch_graph":"https://pith.science/api/pith-number/ARBFFBDNZ3KZRZMIP7D7AYFO5L/graph.json","fetch_events":"https://pith.science/api/pith-number/ARBFFBDNZ3KZRZMIP7D7AYFO5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L/action/storage_attestation","attest_author":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L/action/author_attestation","sign_citation":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L/action/citation_signature","submit_replication":"https://pith.science/pith/ARBFFBDNZ3KZRZMIP7D7AYFO5L/action/replication_record"}},"created_at":"2026-06-23T01:11:55.812112+00:00","updated_at":"2026-06-23T01:11:55.812112+00:00"}